Related papers: Minimum Spanning trees with Neighborhoods
Considering a graph with unknown weights, can we find the shortest path for a pair of nodes if we know the minimal Steiner trees associated with some subset of nodes? That is, with respect to a fixed latent decision-making system (e.g., a…
Neighborhood finders and nearest neighbor queries are fundamental parts of sampling based motion planning algorithms. Using different distance metrics or otherwise changing the definition of a neighborhood produces different algorithms with…
In this work, we study the tensor ring decomposition and its associated numerical algorithms. We establish a sharp transition of algorithmic difficulty of the optimization problem as the bond dimension increases: On one hand, we show the…
In the context of algorithm theory, various studies have been conducted on spanning trees with desirable properties. In this paper, we consider the \textsc{Minimum Cover Spanning Tree} problem (MCST for short). Given a graph $G$ and a…
In this article we extend the computational geometric curve reconstruction approach to curves in Riemannian manifolds. We prove that the minimal spanning tree, given a sufficiently dense sample, correctly reconstructs the smooth arcs and…
For a connected graph, a vertex separator is a set of vertices whose removal creates at least two components. A vertex separator $S$ is minimal if it contains no other separator as a strict subset and a minimum vertex separator is a minimal…
We prove that, if $m$ is sufficiently large, every graph on $m+1$ vertices that has a universal vertex and minimum degree at least $\lfloor \frac{2m}{3} \rfloor$ contains each tree $T$ with $m$ edges as a subgraph. Our result confirms, for…
Edit distances between merge trees of scalar fields have many applications in scientific visualization, such as ensemble analysis, feature tracking or symmetry detection. In this paper, we propose branch mappings, a novel approach to the…
Due to its broad applications in practice, the minimum spanning tree problem and its all kinds of variations have been studied extensively during the last decades, for which a host of efficient exact and heuristic algorithms have been…
We introduce a family of numerical algorithms for the solution of linear system in higher dimensions with the matrix and right hand side given and the solution sought in the tensor train format. The proposed methods are rank--adaptive and…
The mutational heterogeneity of tumours can be described with a tree representing the evolutionary history of the tumour. With noisy sequencing data there may be uncertainty in the inferred tree structure, while we may also wish to study…
We consider the neighborhood tree induced by alternating the use of different neighborhood structures within a local search descent. We investigate the issue of designing a search strategy operating at the neighborhood tree level by…
Many real world data sets exhibit an embedding of low-dimensional structure in a high-dimensional manifold. Examples include images, videos and internet traffic data. It is of great significance to reduce the storage requirements and…
The class of self-nested trees presents remarkable compression properties because of the systematic repetition of subtrees in their structure. In this paper, we provide a better combinatorial characterization of this specific family of…
The solutions to a large class of semi-linear parabolic PDEs are given in terms of expectations of suitable functionals of a tree of branching particles. A sufficient, and in some cases necessary, condition is given for the integrability of…
In the laminar-constrained spanning tree problem, the goal is to find a minimum-cost spanning tree which respects upper bounds on the number of times each cut in a given laminar family is crossed. This generalizes the well-studied…
We consider the stochastic geometry model where the location of each node is a random point in a given metric space, or the existence of each node is uncertain. We study the problems of computing the expected lengths of several…
Formulations of graph algorithms using sparse linear algebra have yielded highly scalable distributed algorithms for problems such as connectivity and shortest path computation. We develop the first formulation of the Awerbuch-Shiloach…
In this paper, we study two examples of minimum weight random graphs with edge constraints. First we consider the complete graph on ${n}$ vertices equipped with uniformly heavy edge weights and use iteration methods to obtain deviation…
In this paper and a companion paper, we prove that, if $m$ is sufficiently large, every graph on $m+1$ vertices that has a universal vertex and minimum degree at least $\lfloor \frac{2m}{3} \rfloor$ contains each tree $T$ with $m$ edges as…